Estimation of Geographically Weighted Regression With Fixed Kernel Gaussian

Abstract

In spatial analysis, the relationship between predictor and response variables is often not uniform across regions, a condition known as spatial heterogeneity. Global regression models such as Ordinary Least Squares (OLS) assume that regression parameters are constant across all locations, meaning that the effects of independent variables are considered identical for every observational unit. This assumption is often unrealistic because it does not account for differences in regional characteristics. If spatial heterogeneity is ignored, model estimates may become less accurate and fail to explain local variations adequately. Geographically Weighted Regression (GWR) is a model that allows regression parameters to vary according to geographic location. Under this approach, each region obtains its own local parameter estimates, enabling the model to capture spatially varying relationships more flexibly. The results indicate that the AIC value of the GWR model with Fixed Gaussian Kernel (347.8637) is smaller than that of the OLS model (382.1161), suggesting that GWR provides a better fit. Empirically, the Human Development Index (HDI) in 53 districts/cities is influenced by Life Expectancy, Expected Years of Schooling, and Per Capita Expenditure, while in 66 districts/cities it is influenced by Life Expectancy, Expected Years of Schooling, Poverty Rate, and Per Capita Expenditure.